System and method for image regularization in inhomogeneous environments using clustering in neural networks

Abstract

A regularization system and method for image restoration in homogeneous or inhomogeneous environments. The system and method includes features similar to a neural network with intermediate levels of structure including a pixel having processing capabilities; clusters consisting of a plurality of interconnected pixels and also having processing capabilities; and an image space comprised of a plurality of interconnected pixels and clusters and also having processing capabilities. The system and method also include means for assigning a regularization parameter to each pixel depending on the local variance of intensity of pixels; decomposing the image space into clusters of pixels, each cluster having the same regularization parameter; imposing a blurring function on each pixel; rapidly forming a regularized image by simultaneous local and global encoding of a regularization matrix onto each pixel directed through a process of gradient energy decent; and a means of assessing the output image.

What is claimed is: 
     
       1. A network of computational units comprising: a first pixel having processing capabilities and the capability of assuming an activity state;   a first cluster including a network of a plurality of interconnected pixels including the first pixel, the first cluster also having processing capabilities;   an image space including a network of interconnected clusters of interconnected pixels including the first cluster, the image space also having processing capabilities;   a mapping module that maps an input image upon the image space;   a variance-measuring module that determines a variance of activity states of a plurality of pixels around the first pixel;   a regularization module that assigns a regularization parameter to the first pixel determined by the variance; and   a cluster-adjusting module that changes the shape of the first cluster to include only a plurality of interconnected pixels, each pixel having a similar regularization parameter assigned to it.   
     
     
       2. The network of computational units of claim 1 further including a blurring module that applies a blurring function to the activity state of the first pixel. 
     
     
       3. The network of computational units of claim 2 further including a weight-assigning module that assigns a weight function to the first pixel as determined by the regularization parameter and the blurring function. 
     
     
       4. The network of computational units of claim 3 further including an intensity-adjusting module that adjusts the activity state of the first pixel. 
     
     
       5. The network of computational units of claim 1 wherein connections exist between both spatially local and distant pixels. 
     
     
       6. The network of computational units of claim 1 wherein connections exist between both spatially local and distant clusters. 
     
     
       7. The network of computational units of claim 1 wherein the image space includes an edge region increasing by at least one pixel the space upon which an input image has been mapped. 
     
     
       8. The network of computational units of claim 1 wherein a plurality of clusters comprising pluralities of pixels is formed based on commonality of regularization parameters. 
     
     
       9. The network of computational units of claim 3 wherein the weight-assigning module selects a weight function from a plurality of weight functions as determined by anticipated characteristics of distortion imposed on the input image. 
     
     
       10. The network of computational units of claim 9 wherein relatively large weights are related to anticipated small local variances and relatively small weights are related to anticipated large local variances. 
     
     
       11. The network of computational units of claim 4 wherein the intensity-adjusting module adjusts the activity state of the first pixel by the process of gradient energy decent. 
     
     
       12. The network of computational units of claim 4 wherein the activity state of the first pixel continues to be adjusted until an intensity-change-measuring module determines that the activity state of the first pixel is not changed by application of the weight function. 
     
     
       13. The network of computational units of claim 4 wherein the activity state of the first pixel continues to be adjusted until an intensity-change-measuring module determines that the activity state of the first pixel and the activity state of at least one other pixel of the plurality of pixels is not changed by application of the weight function. 
     
     
       14. A network of computational units comprising: a first pixel having processing capabilities and the capability of assuming an activity state;   a first cluster including a network of a plurality of interconnected pixels including the first pixel, the first cluster also having processing capabilities;   an image space including a network of interconnected clusters of interconnected pixels including the first cluster, the image space also having processing capabilities;   means for mapping an input image upon the image space;   means for determining a variance of activity states of a plurality of pixels around the first pixel;   means for assigning a regularization parameter to the first pixel determined by the variance; and   means for changing the shape of the first cluster to include only a plurality of interconnected pixels, each pixel having a similar regularization parameter assigned to it.   
     
     
       15. The network of computational units of claim 14 further including: means for applying a blurring function to the activity state of the first pixel;   means for assigning to the first pixel a weight function determined by the regularization parameter and the blurring function;   means for adjusting the activity state of the first pixel;   means for selecting the weight function from a plurality of weight functions determined by anticipated characteristics of distortion imposed on the input image; and   means for continuing to adjust the activity state of the first pixel until the activity state of the first pixel and the activity state of at least one other pixel of the plurality of pixels is no changed by application of the weight function.   
     
     
       16. A method for regularizing an input image distorted by noise comprising the steps of: forming a first pixel having processing capabilities and capable of having an activity state;   forming a first cluster including a network of a plurality of interconnected pixels including the first pixel, the cluster also having processing capabilities;   forming an image space including a network of interconnected clusters of interconnected pixels including the first cluster, the image space also having processing capabilities;   mapping an input image upon the image space;   determining a variance of activity states of a plurality of pixels around the first pixel;   assigning a regularization parameter to the first pixel determined by the variance; and   changing a shape of the first cluster to include only a plurality of interconnected pixels each having a similar regularization parameter assigned to it.   
     
     
       17. The method of claim 16 further comprising the steps of: determining a blurring function;   determining a size of a blurring region over which the blurring function can be applied to the activity state of the first pixel;   applying the blurring function to the activity state of the first pixel;   determining a plurality of weight functions;   assigning to the first pixel a weight function determined by the regularization parameter and the blurring function;   calculating the weighted inputs to the first pixel;   changing the activity state of the first pixel based on the weighted inputs;   determining a computational energy change of the first pixel due to the change in the activity state;   adjusting the activity state of the first pixel to decrease the computational energy; and   repeating the foregoing steps unless adjusting the activity state of the first pixel does not decrease the computational energy.   
     
     
       18. The method of claim 17 wherein the last step consists of repeating the foregoing steps unless adjusting the activity state of the first pixel and at least one other pixel does not decrease the computational energy. 
     
     
       19. The method of claim 17 or claim 18 further comprising the step of: specifying the context in which the input image was distorted.   
     
     
       20. The method of claim 17 or claim 18 further comprising the step of: adding an edge region consisting of at least one pixel to the image space.